1. Field of the Invention
The invention pertains to the art of toroidal shaped electrolytic accelerometers or tilt sensors and more particularly to devices of this type which include means for providing temperature compensation.
2. Description of the Prior Art
The subject invention is an improvement over the following U.S. Pat. Nos.: 3,823,486 entitled "Toroidal Electrolytic Sensor and Method of Manufacture", issued in the name of Bhat et al on July 16, 1974; 3,604,275, issued in the name of T. S. Fox et al on Sept. 14, 1971 and entitled "Toroidal Electrolytic Sensor"; and 3,171,213, entitled "Electrolytic Tilt Sensor", issued in the name of R. E. Swarts et al on Mar. 2, 1965, all of said patents being assigned to the assignee of the subject application.
U.S. Pat. No. 3,171,213 discloses a device comprised of a housing having a toroidal shaped chamber formed by a cylindrical housing having an inner tube disposed along the axis of tilt of the housing. The inner tube includes an insulative rod disposed within an outer conductive portion which forms a common terminal. Affixed to the interior surface of the housing are two arcuate shaped terminals or conductors arranged in opposed angular relation with respect to one another at a fixed radial spacing with respect to the longitudinal tube. An electrolytic liquid half fills the toroidal shaped inner chamber of the sensor. This device is designed and constructed so that its operation is characterized by a fundamental physical relationship between the angle of tilt and the areas of the electrodes immersed in the electrolytic solution. The principal of operation states that the difference in immersed areas between the respective arcuately disposed inner conductive terminals is linearly proportional to the angle of tilt. This is expressed mathematically as follows: EQU (A.sub.L - A.sub.R)= K.theta. (1)
where:
A.sub.l = immersed area of the electrode in the left conductance cell. PA0 A.sub.r = immersed area of the electrode in the right conductance cell. PA0 K= a proportionality constant relating to the geometry of the electrodes expressed in degrees per unit area. PA0 .theta. = angle of tilt. PA0 .delta. = resistivity of the electrolytic solution expressed as ohms per unit area per unit distance. PA0 A= immersed area of an electrode.
It is apparent from the foregoing equation that if an increment of electrode area is added to or subtracted from both conductance cells, the equality of the equation is maintained. This implies that the operation of the device is inherently insensitive to electrolytic fluid level change. Variations in fluid level may result from different effects including leakage of the fluid from the sensor which will lower the level of the fluid, hangup of the fluid within the sensor which will have the same effect, gas bubble entrapment within the fluid which will increase the fluid level in the sensor and effects resulting from the temperature expansion characteristic of the housing and the fluid. It will be noted that the device described by equation (1) is insensitive to the fluid level changes resulting from thermal expansion properties of the fluid in the housing because these changes will not effect the equality of the equation.
However, the practical implementation of the device described in U.S. Pat. No. 3,171,213, in accordance with equation (1) requires an electrical circuit means whereby a measurable voltage can be developed which is proportional to the left hand side of the equation. The circuit must provide a proportional functional relationship between the measurable voltage and the tilt angle of the device represented by the right hand side of the equation. The resistance value of the two conductance cells is the parameter commonly used to represent the immersed area. The resistance versus area relationship to be used is described in the following equation: ##EQU1## where D= distance between electrodes in the conductance cell.
Solving the foregoing equation for A and substituting the resulting relationship into equation (1) with appropriate subscripts, the following equation results: EQU (l/R.sub. L - l/R.sub. R) D.delta. = K.theta. (3)
this equation is the characteristic equation of toroidal accelerometers and tilt sensors known in the prior art. A circuit which will permit a voltage to be measured which is proportional to the quantity (l/R.sub. L - l/R.sub. R) or functionally related to this quantity so that a voltage and angle can be equated is shown in FIG. 1. It will be shown in the following analysis that the toroidal accelerometer known in the prior art and the electrical circuit used in connection therewith does not result in a sensor which is insensitive to the effects of temperature.
A circuit typically used with the electrolytic tilt sensor disclosed by R. E. Swarts et al is shown in FIG. 1. The voltage across the output resistor R is expressed as follows: EQU V= I.sub.T (R) (4) EQU i.sub.t = i.sub.l + i.sub.r ( 5) EQU i.sub.l = (e-v/r.sub.l) (6) EQU i.sub.r = (-e-v/r.sub.r) (7)
substituting equations (6) and (7) into equation (5) and substituting the result thereof into equation (4) yields: ##EQU2##
First transposing terms to obtain: ##EQU3## Then substituting this equation into equation (3) yields:
Using the area relationship for resistance of the cells, in equation (2) and solving for the voltage results in the following equation: ##EQU4##
An inspection of the foregoing equation shows there are two quantities in the equation which vary with temperature, i.e., the electrolytic resistivity (.delta.) and the quantity (A.sub.L + A.sub.R).
The electrolytic resistivity (.delta.) typically decreases with increasing temperature and the quantity (A.sub.L + A.sub.R) which represents the total immersed areas of the electrodes is temperature sensitive due to fluid expansion and contraction. In practice, the fluid has a greater volumetric thermal expansion than the housing material used to contain it. As a result, the fluid level in the toroidal shaped cavity will rise with increasing temperature. Therefore, it is apparent that the value of the load resistor (R) may be selected in order to maintain the most constant value of the denominator in the above equation over a given range of temperature. Thus, the circuit shown in FIG. 1 provides a means of limited temperature compensation for the toroidal accelerometer or tilt sensor device as known to the prior art.
In U.S. Pat. No. 3,604,275 the toroidal electrolytic sensor included a hollow tubular member of glass having disposed therein substantially identical arcuate-shaped pairs of electrodes diametrically positioned within the member. This sensor was stated as enjoying inherent temperature compensation due to its symmetrical configuration. Expansion and contraction of the electrolyte occurred symmetrically with respect to both pairs of electrodes and therefore the null electrical characteristics remained virtually constant and verticality drift due to temperature changes from the calibration temperature were minimized.
In U.S. Pat. No. 3,823,486 it was noted that the improved structural characteristics of the sensor eliminated the requirement of extra fluid to fill up the lower portions of the device as required in the accelerometer disclosed by Fox et al. As a result, the device disclosed by Bhat et al was less susceptible to temperature variations for a given linear angular range of the device. Although the configuration disclosed by Bhat et al is less susceptible to temperature variations, neither this device nor the prior art devices of Fox et al or Swarts et al included means which effectively compensated the effects due to temperature produced on the two quantities in the foregoing equation, i.e., electrolyte resistivity (.delta.) and the quantity (A.sub.L + A.sub.R) which represents the total immersed areas of the electrodes.
There are, however, electrical circuits known in the prior art which employ an operational amplifier and provide a voltage (V) which is linearly related to the quantity (l/R.sub. L -l/R.sub. R) in the characteristic equation of the device expressed in equation (3). One such typical circuit is disclosed on page 210, FIGS. 6, 8 of "Operational Amplifiers-- Design and Applications" by Graeme, Tobey and Huelsman, published 1971 by McGraw Hill Book Company. A similar type circuit is shown in U.S. Pat. No. 2,978,638 entitled "Coercion-Free Capacitance Pick-off", issued Apr. 4, 1961 and assigned to the present assignee. This typical prior art circuit is shown in FIG. 3 and it includes an operational amplifier which provides an output voltage V mathematically expressed as: EQU V= ER (l/R.sub.L - l/R.sub.R) (12)
solving for the expression (l/R.sub.L - l/R.sub.R) and substituting the result into equation (3) above yields the following relationship for the voltage V: ##EQU5##
It is seen from the foregoing equation that all terms in the coefficient of .theta. on the right side of the equation are basically insensitive to temperature with the exception of the electrolytic resistivity (.delta.). Since this term is contained in the characteristic equation for this type of sensor as described by equation (3) it can be expected to appear in some form or other in the voltage versus tilt angle function derived from any electrical circuit used to provide the output voltage V in accordance with equation (3).
The subject invention provides means in this type of sensor which in combination with a suitable electronic circuit compensates for variations in output voltage produced by the effect of temperature on the electrolyte resistivity (.delta.).